Inputs
Example data table
| Scenario | f₀ (mm/hr) | fc (mm/hr) | k (1/hr) | t (hr) | i (mm/hr) | f(t) (mm/hr) | F(t) (mm) |
|---|---|---|---|---|---|---|---|
| Loam after dry spell | 75 | 12 | 3.2 | 1.5 | 40 | ≈ 12.518 | ≈ 37.525 |
| Sandy soil, fast decay | 160 | 35 | 2.0 | 1.0 | 90 | ≈ 51.917 | ≈ 89.042 |
Values are illustrative. Calibrate f₀, fc, and k using field or lab measurements.
Formula used
Horton infiltration capacity models how infiltration decreases with time during wetting:
f(t) = fc + (f0 − fc) · e−k t
- f(t): infiltration capacity at time t
- f₀: initial capacity at the start of wetting
- fc: long-time (final) capacity
- k: decay constant (typically in 1/hr)
Cumulative infiltration capacity is the integral of f(t) from 0 to t:
F(t) = fc t + (f0 − fc)/k · (1 − e−k t)
Supply-limited option: If rainfall (or supply) rate i is provided, the actual intake rate is:
fact(t) = min(i, f(t))
How to use this calculator
- Enter f₀, fc, and k from calibration data.
- Select the rate and time units you recorded in the field.
- Set analysis time t and table step Δt for the time series.
- Enable the supply limit and enter i if rainfall is known.
- Press Calculate to view results above this form.
- Download CSV or PDF to archive the calculation and table.
Practical notes
- If f₀ ≈ fc, infiltration is nearly steady.
- Large k means rapid decline after wetting begins.
- For very small Δt, tables can be long; prefer downloads.
- Use consistent units: rate for f₀, fc, i, time for t, Δt.
Professional article
1) Why infiltration capacity declines during storms
Early rainfall often infiltrates quickly because pores are empty and suction is strong. As wetting continues, pore air escape becomes harder, the near-surface layer can seal, and the hydraulic gradient weakens. Horton captures this event-scale decline with an exponential approach to a steady rate.
2) Interpreting f₀, fc, and k
f₀ represents the starting infiltration capacity at wetting onset, influenced by crusting, macropores, and antecedent moisture. fc is the late-time capacity after the soil is wetted. k controls how quickly capacity drops toward fc.
3) Practical parameter ranges
For event modeling, f₀ is often tens to a few hundred mm/hr, while fc may be a few mm/hr for compacted fines and several tens of mm/hr for sandy or well-structured soils. A common starting range for k is 0.5–5 1/hr.
4) Using cumulative infiltration in water balance
The integral F(t) provides cumulative infiltration depth, useful for sizing infiltration basins, checking storage drawdown, and estimating runoff potential. Comparing rainfall depth to F(t) highlights when rainfall exceeds intake, a key trigger for surface ponding and overland flow.
5) Supply-limited intake with rainfall intensity i
Actual infiltration cannot exceed the available water supply. When rainfall intensity i is lower than capacity, intake equals i. As f(t) declines, the soil may become limiting. Using min(i, f(t)) separates rainfall-controlled periods from infiltration-controlled periods.
6) Calibration from measurements
Estimate fc from late-time steady infiltration, infer f₀ from early readings, and tune k to match the transition. Data can come from infiltrometers, rainfall–runoff records, or basin drawdown curves. Recalibrate after land-use change, compaction, or sediment deposition.
7) Choosing Δt for stable tables
The table reports capacity, actual rate, and cumulative depths at increments Δt. For event summaries, choose Δt so 20–50 steps cover the duration; smaller steps improve the numerical cumulative actual value. For long events, exporting the table is cleaner than scrolling.
8) Engineering interpretation and limitations
Horton is simple, interpretable, and widely used in drainage and catchment simulations, but its parameters are effective event descriptors, not permanent soil constants. Use conservative values for design storms, apply the supply limit when rainfall is known, and validate outputs against observed ponding or runoff behavior.
FAQs
1) What is Horton infiltration used for?
It estimates how soil intake capacity declines during a rainfall event, supporting stormwater balance, runoff prediction, and infiltration facility sizing. It is especially useful for event-based hydrologic calculations.
2) What units should I use for k?
Use inverse time units consistent with your time input. This calculator assumes k is in 1/hr internally, so if you enter time in minutes or seconds, the tool converts time to hours while keeping k in 1/hr.
3) Why must f₀ be greater than or equal to fc?
Horton decay represents a decreasing capacity approaching a steady value. If f₀ is below fc, the curve would increase over time, which contradicts the standard wetting behavior the model intends to capture.
4) What does the supply limit option do?
It caps infiltration by rainfall or available water rate i, using min(i, f(t)). This prevents unrealistic infiltration when capacity is high but rainfall is low, improving event realism.
5) How do I choose Δt for the table?
Pick Δt small enough to represent the curve smoothly, such as event duration divided by 20–50. If you only need a single-time result, Δt mainly affects the displayed table and cumulative actual value.
6) Are f₀ and fc soil properties?
They are effective event parameters, influenced by soil texture, structure, crusting, and antecedent moisture. They can vary between storms and sites, so calibration from local observations is recommended.
7) Why can cumulative actual infiltration differ from F(t)?
F(t) is the analytic integral of capacity. Actual infiltration may be smaller when rainfall i is limiting. The calculator integrates min(i, f(t)) over time to estimate a realistic cumulative depth.
Use measured parameters; validate outputs against site observations always.